The 27-year-old succeeded Jon Petrie after injury to the Glasgow number eight ruled him out of the matches with Argentina, Samoa and New Zealand.
And Hadden believes White will overcome the additional burden of captaincy to produce more fine displays in a dark blue shirt.
"There is no guarantee you are going to sustain your form," Hadden said. "There are so many aspects to the captaincy but Jason produced his three best Scotland performances in November.
"His work-rate has increased dramatically and that is his way of leading from the front.
"If we can guarantee that is the level he will perform at throughout the Six Nations it is as good a reason as any to give him the captaincy.
"Jason is different from Jon Petrie, but he is very well respected by the players and he will grow into the role.
"He hasn't done a lot of captaincy but he has had a taste of it now."
White is relishing the chance to lead the team out again next month.
He said: "I really enjoyed being captain in the November Tests. To be asked to lead my country again is a vote of confidence from Frank.
"Personally, and as a group of players, we cannot wait for the championship to start and we look forward to putting in some better performances."
Hadden believes his team are in good stead for the championship opener at Murrayfield.
Scotland were expected to be overwhelmed when the all-conquering All Blacks arrived in Edinburgh in November seeking a Grand Slam against the home nations.
However, a spirited display by the Scots ensured they were far from outclassed despite an eventual 29-10 defeat.
Hadden said: "I am confident we will play well and give a good account of ourselves in the Six Nations.
"What we need to do is build on what we have started. Our belief has generated some momentum.
"Momentum does not count for a lot unless we put some clear evidence of that into place in the Six Nations."
Hadden has also called on the Murrayfield crowd to play their part in maintaining that momentum for the games against France and England.
"If we can fill Murrayfield for the visit of the French, it gives us a huge chance," Hadden added.
"If we can sell out that game it will give us a tremendous chance of beating France.
"The fans are such an influence because we know how intimidating it can be for away sides - how hard it can be at the Millennium Stadium for example.
"It would be great if we could generate that atmosphere at Murrayfield so teams really don't enjoy coming here."